The question asks for the SI unit of electrical resistance. To answer this, we need to recall the fundamental SI units for various electrical quantities.
Correct Option: B) Ohm is the SI unit of electrical resistance.
The question describes the relationship between the electrical resistance of a uniform conductor and its physical dimensions (length and cross-sectional area). We need to identify the correct formula that expresses this relationship, which also involves a material-specific property called resistivity.
Understand the given relationships: The problem states that the electrical resistance (\(R\)) of a uniform conductor is directly proportional to its length (\(L\)). This can be written as:
\[ R \propto L \]It also states that the electrical resistance (\(R\)) is inversely proportional to its cross-sectional area (\(A\)). This can be written as:
\[ R \propto \frac{1}{A} \]Combine the proportionalities: Combining both relationships, we get:
\[ R \propto \frac{L}{A} \]Introduce the constant of proportionality: To convert this proportionality into an equation, we introduce a constant of proportionality. This constant is known as the electrical resistivity, denoted by the Greek letter rho (\(\rho\)). Resistivity is a fundamental property of the material of the conductor.
\[ R = \rho \frac{L}{A} \]This formula accurately represents the electrical resistance of a uniform conductor based on its material's resistivity, its length, and its cross-sectional area.
D) R = ρL/A — This formula correctly shows that resistance is directly proportional to length (\(L\)) and resistivity (\(\rho\)), and inversely proportional to the cross-sectional area (\(A\)).
The question asks about the general relationship between electrical resistance and temperature for most metallic conductors. This is a fundamental concept in physics and electrical engineering.
Correct Option: A) Resistance generally increases with increasing temperature. This is because higher temperatures cause increased thermal vibrations of atoms in the metal lattice, leading to more frequent collisions with free electrons, thereby impeding current flow and increasing resistance.
The question asks about the total (equivalent) resistance when two or more resistors are connected in series. We need to recall the fundamental rules for calculating equivalent resistance in series and parallel circuits.
C) The simple sum of the individual resistances. As derived above, when resistors are connected in series, the equivalent resistance is the direct sum of their individual resistance values. This increases the total resistance of the circuit.
This question asks about the formula for calculating the total (equivalent) resistance when two or more resistors are connected in parallel. We need to recall the fundamental laws of electrical circuits, specifically how resistances combine in parallel.
A) The sum of the reciprocals of the individual resistances (1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ...) is the correct formula for calculating the total (equivalent) resistance when resistors are connected in parallel.
To find the current flowing through a series circuit, we first need to calculate the total equivalent resistance of the resistors connected in series. Once the total resistance is known, we can use Ohm's Law, which states that current is equal to potential difference divided by resistance.
When resistors are connected in series, the total resistance is the sum of individual resistances.
\[ R_{\text{eq}} = R_1 + R_2 + R_3 \]\[ R_{\text{eq}} = 2 \, \Omega + 3 \, \Omega + 5 \, \Omega \]\[ R_{\text{eq}} = 10 \, \Omega \]Ohm's Law states \(V = I \times R\), so \(I = \frac{V}{R_{\text{eq}}}\).
\[ I = \frac{10 \, \text{V}}{10 \, \Omega} \]\[ I = 1 \, \text{A} \]Correct Option: C) 1 A